String junctions for arbitrary Lie-algebra representations

Abstract

We consider string junctions with endpoints on a set of branes of IIB string theory defining an ADE-type gauge Lie algebra. We show how to characterize uniquely equivalence classes of junctions related by string/brane crossing through invariant charges that count the effective number of prongs ending on each brane. Each equivalence class defines a point on a lattice of junctions. We define a metric on this lattice arising from the intersection pairing of junctions, and use self-intersection to identify junctions in the adjoint and fundamental representations of all ADE algebras. This information suffices to determine the relation between junction lattices and the Lie-algebra weight lattices. Arbitrary representations are built by allowing junctions with asymptotic ( p, q) charges, on which the group of conjugacy classes of representations is represented additively. One can view the ( p, q) asymptotic charges as Dynkin labels associated to two new fundamental weight vectors.